CN114757036B - River section automatic interpolation method based on successive approximation method - Google Patents
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Abstract
The invention discloses a river section automatic interpolation method based on a successive approximation method, which belongs to the technical field of river hydrodynamic force numerical simulation. The method comprises the following steps: step 1: establishing a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model by taking the Nash coefficient sum maximum of the observed section water level and flow hydrologic factors as an objective function and taking the water level or flow error and section spacing as constraint conditions; step 2: determining a parameter value range of an automatic interpolation optimization model of the river section; step 3: and solving the river section automatic interpolation optimization model by adopting a pattern positioning mode or a successive approximation method of a pattern setting mode. The invention realizes the automatic optimization of parameters such as the number, the position, the shape, the river course roughness and the like of the river course interpolation sections in the mountain area lacking the topography data; subjective randomness and uncertainty of manual debugging can be avoided, and simulation precision is improved.
Description
Technical Field
The invention relates to the technical field of river hydrodynamic force numerical simulation, in particular to a river section automatic interpolation method based on a successive approximation method.
Background
River topography data is an important basis for modeling river hydrodynamic force, but river topography data is insufficient or rough. Therefore, limited topography and hydrologic data can be fully utilized, and sections can be appropriately inserted to better simulate the along-path water level and flow change condition of the river channel.
At present, most of the prior art adopts a manual test algorithm, firstly, initial values of the shape and the position of the interpolation section are given, then the initial values are substituted into a one-dimensional unsteady flow mathematical model for calculation, the difference between the calculated value and the measured value of the water level flow of the observation section is compared, then the values of the shape and the position parameters of the interpolation section are manually adjusted for calculation again, and the process is repeated until the difference between the calculated value and the measured value of the water level flow of the observation section meets the precision requirement, so that the optimal shape and the position parameters of the interpolation section are selected. The manual trial algorithm is adopted for parameter adjustment, so that time and labor are wasted, the workload is high, the experience and the randomness are high, and the precision is difficult to guarantee. Especially, the interaction between the shape and the position of the interpolation section is considered when the interpolation section is needed, the calculation difficulty is high, and the optimal shape and position parameters of the interpolation section cannot be found out by a manual trial algorithm, so that the fitting error between the water level flow calculated value and the measured value of the observation section is small. Therefore, it is necessary to study a mature and effective river section automatic interpolation method.
Aiming at the problem of the artificial trial algorithm in the river section interpolation, a river section automatic interpolation method is needed based on the successive approximation algorithm, and under the condition of lacking topography data, the automatic interpolation of the river section is realized, so that the optimal interpolation section shape and position parameters are obtained. Compared with manual parameter adjustment, the computer intelligent parameter adjustment is more time-saving and labor-saving, subjective randomness and uncertainty of manual adjustment can be avoided, and simulation precision is improved.
Disclosure of Invention
The invention aims to provide a river section automatic interpolation method based on a successive approximation method, which is characterized by comprising the following steps of:
step 1: establishing a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model by taking the maximum sum of Nash coefficients of observed section water level and flow hydrologic factors as an objective function and taking water level, flow error and section spacing as constraint conditions;
step 2: according to the length, width and ratio drop of the river channel, determining the parameter value range of the automatic interpolation optimization model of the river channel section; the parameters comprise river course roughness, the number of the inserted sections, the positions of the inserted sections and the shape parameters of the inserted sections, wherein the shape parameters of the inserted sections comprise section bottom width, river bottom elevation and slope coefficients;
step 3: according to a parallel solving method based on a successive approximation method, adopting a shape-based positioning calculation mode or a shape-based calculation mode to solve the river section automatic interpolation optimization model.
The river section automatic interpolation optimization model in the step 1 is as follows:
objective function:
wherein i is the serial number of the observation section; n is the total number of observation sections; NSE (i) is a nash coefficient value of the observation section i, specifically:
wherein T is the calculation period, y t (i) The measured value of the water level or the flow of the section i;
the average value of the measured sequence of the water level or the flow of the section i; />
Calculating a value for the water level or flow of the section i;
constraint conditions:
wherein: abs is an absolute function, ε i Maximum water level or flow error for the ith section;
L min ≤L(k)≤L max (4)
wherein L (k) is the section distance between the inserted section k and the previous section; l (L) max For a given maximum section spacing; l (L) min For a given minimum section spacing, 0 is taken.
The successive approximation method-based parallel solving method in the step 3 specifically comprises the following steps:
step S1: dispersing the parameters, and setting the number of the interpolation sections as k 1 The number of the inserted section positions is k 2 The number of the bottom widths of the sections in the shape of the inserted section is k 3 The number of river bottom elevations is k 4 Edges(s)The number of slope coefficients is k 5 The number of the river course roughness is k 6 Then share
A combination of parameters;
step S2: fixing the number of the inserted sections, the positions of the inserted sections and the value of the river course roughness, and only taking the shape of each inserted section
Substituting the individual parameter combinations into a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model to perform successive optimization;
step S3: carrying out parallelization processing on a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model by combining with an OpenMP compiling processing technology designed for single-host multi-CPU parallel computation, and carrying out combination number in the step S2
Assigned to different threads for simultaneous computation.
The shape positioning calculation mode in the step 3 is to optimize the shape of the interpolation section first and then determine the position of the interpolation section: firstly, assuming equidistant distribution of the interpolation sections, then, carrying out optimization calculation on the shape of each interpolation section according to an objective function to obtain a section bottom width, a river bottom elevation and a slope coefficient, and finally, carrying out optimization calculation on the section spacing of each interpolation section to obtain the optimal spacing of each interpolation section; the method specifically comprises the following steps:
step A1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i ，i＝1,2,…,6；
Step A2: determining the river course roughness value;
step A3: determining the number k of the inserted sections 1 The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step A4: setting the optimizing iteration times L=1 of the section shape, and inserting the section j=1;
step A5: to be inserted into section j
Substituting the individual shape parameter combination schemes into the model, carrying out parallel optimizing calculation by combining the river section automatic interpolation optimizing model, and then turning to the step A6;
step A6: fixing the optimized shape parameters of the interpolation section, and then turning to the step A7;
step A7: judging whether the optimizing number of the interpolation section j is equal to the number k of the interpolation sections 1 If not, let j=j+1, go to step A5 again; if yes, obtaining the shape optimization result of each interpolation section and the current shape iteration objective function value F L Turning to step A8;
step A8: judging whether the cross section shape optimizing iteration times L is greater than 1, if not, making L=L+1, and then turning to the step A5; if yes, go to step A9;
step A9: judgment F L And last shape iteration objective function value F L-1 If the two iteration results meet the convergence condition, if not, making L=L+1, and then turning to the step A5; if yes, obtaining an optimal scheme of the shapes of the various inserting sections under the current river course roughness and the number of the inserting sections;
step A10: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step A11: fixing the shape of each interpolation section, and for k of interpolation section j 2 Substituting the position parameter scheme into a model, and carrying out parallel optimizing calculation by combining with an automatic interpolation optimizing model of the river section; turning to step A12;
step A12: fixing the optimized position parameters of the interpolation section; turning to step A13;
step A13: judging whether the interpolation section j is equal to k 2 If not, let j=j+1, go to step a11 again; if yes, obtaining the position optimization result of each interpolation section and the current position iteration objective function value F M Turning to step A14;
step A14: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step A11; if yes, go to step A15;
step A15: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A11; if yes, obtaining the optimal scheme of the shape and the position of each interpolation section under the current river course roughness and the number of the interpolation sections, and then turning to the step A16;
step A16: sequentially changing the number of the interpolation sections and the river course roughness value, and repeating the steps A1 to A15 to obtain the optimal scheme of the shape and the position of each interpolation section under the scheme of changing the number of the interpolation sections and the river course roughness value.
The bit setting calculation mode in the step 3 is to firstly determine the position of the interpolation section and then optimize the shape of the interpolation section: firstly, setting a plurality of interpolation sections with the same shape, setting the shapes of the sections as rectangles, then, only changing the river bottom elevation of each interpolation section to perform optimizing calculation, merging the sections with similar river bottom elevation, selecting representative positions, and finally, optimizing the shapes of each interpolation section to obtain the optimal shape parameters of each interpolation section; the method specifically comprises the following steps:
step B1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i I=1, 2, …, 6;
step B2: determining the river course roughness value;
step B3: determining the number k of rectangular interpolation sections Moment (V) The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step B4: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step B5: substituting the river bottom elevation calculation scheme of the interpolation section j into the model, carrying out parallel optimization calculation by combining with the river section automatic interpolation optimization model, and then turning to the step B6;
step B6: fixing the optimized river bottom elevation of the inserted section, and then turning to the step B7;
step B7: judging whether the optimizing number of the interpolation section jEqual to the number k of rectangular interpolation sections Moment (V) If not, let j=j+1, go to step B5 again; if yes, obtaining river bottom elevation optimization results of each interpolation section and the current position iteration objective function value F M Turning to step B8;
step B8: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step B5; if yes, go to step B9;
step B9: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A5; if so, obtaining the river bottom elevation change condition of each interpolation section under the current river course roughness and the number of the interpolation sections, merging sections with similar river bottom elevations, and selecting a representative position;
step B10: setting the optimizing iteration times L=1 of the section shape, and inserting the section j=1;
step B11: determining the number k of the inserted sections 1 Substituting the shape parameter scheme of the interpolation section j into the model, carrying out parallel optimization calculation by combining with the river section automatic interpolation optimization model, and then turning to the step B12;
step B12: fixing the optimized interpolation section shape parameters, and then turning to the step B13;
step B13: judging whether the interpolation section j is equal to k 1 If not, let j=j+1, go to step B11; if yes, obtaining the position optimization result of each interpolation section and the current shape iteration objective function value F L Turning to step B14;
step B14: judging whether the cross section shape optimizing iteration times L is greater than 1, if not, making L=L+1, and then turning to the step B11; if yes, go to step B15;
step B15: judgment F L And last shape iteration objective function value F L-1 If the two iteration results meet the convergence condition, if not, making L=L+1, and then turning to the step B11; if yes, obtaining the optimal scheme of the shape and the position of each interpolation section under the current river course roughness and the number of the interpolation sections;
step B16: sequentially changing the number of the interpolation sections and the river course roughness value, and repeating the steps B1-B15 to obtain the optimal scheme of the shape and the position of each interpolation section under the scheme of changing the number of the interpolation sections and the river course roughness value.
The invention has the beneficial effects that:
1. the invention realizes the automatic optimization of parameters such as the number, the position, the shape, the river course roughness and the like of the river course interpolation sections in the mountain area lacking the topography data;
2. the method for solving the problems in parallel based on the successive approximation method reduces the calculated amount and the calculation difficulty;
3. the model built by the invention has certain universality for generalized sections (such as rectangles, trapezoids, triangles and the like) with regular section shapes, and the optimal interpolation scheme can be obtained only by modifying the values of the shape parameters; compared with manual parameter adjustment, the method is time-saving and labor-saving, can avoid subjective randomness and uncertainty of manual debugging, and improves simulation precision;
4. the established river channel interpolation section automatic optimization model has good parallel computing conditions, and the computing program is subjected to parallelization processing through an OpenMP compiling processing technology, so that the computing efficiency can be greatly improved, and the computing time can be saved.
Drawings
FIG. 1 is a flow chart of a river section automatic interpolation method based on a successive approximation method;
FIG. 2 is a computational flow diagram of a "shape location" mode;
FIG. 3 is a computational flow diagram in "bit-shaping" mode;
FIG. 4 shows an interpolation section (D0) 1 ～D0 5 ) A position diagram;
FIG. 5 is a graph of flow process for section D0;
FIG. 6 is a graph of the water level process at section D12;
FIG. 7 is a schematic diagram of a cross-sectional shape variation;
FIG. 8 is a graph showing the comparison of measured and calculated values of the water level at section D0 in the "positioning" mode;
FIG. 9 is a graph comparing measured and calculated flow rates of section D2 in "shape-locating" mode;
FIG. 10 is a graph showing the comparison of measured and calculated values of the water level at section D4 in the "positioning" mode;
FIG. 11 is a graph of the variation of the river bottom elevation parameters of 117 interpolation sections;
FIG. 12 is a graph showing the comparison of measured and calculated values of the water level at section D0 in the "setting" mode;
FIG. 13 is a graph showing the comparison of measured and calculated values of the section flow rate in the "bit-set" mode D2;
FIG. 14 is a graph showing the comparison of measured and calculated values of the water level at section D4 in the "setting" mode.
Detailed Description
The invention provides a river section automatic interpolation method based on a successive approximation method, and the method is further described below with reference to drawings and specific embodiments.
FIG. 1 is a flow chart of a river section automatic interpolation method based on a successive approximation method; the method specifically comprises the following steps:
1 model building
And establishing a river channel interpolation section automatic optimization model based on a one-dimensional unsteady flow mathematical model by taking Nash coefficients and maximum values of hydrologic factors such as the water level of an observed section, the flow and the like as an objective function and taking the water level, the flow error and the section spacing as constraint conditions.
1.1 one-dimensional unsteady flow mathematical model
Describing one-dimensional water flow motion of a river channel by adopting a Saint-Venature equation set, wherein a water flow continuous equation and a motion equation are respectively as follows
Wherein: t is time; x is the flow; q is flow; z is the water level; a is the cross-sectional area of water passing; b is river width; r is the hydraulic radius; n is the roughness; v is the average of the cross sectionsA flow rate; q l And u l The components of the lateral inflow and the lateral inflow in the x direction are the unit length of the river reach; alpha 1 For momentum correction coefficient, alpha 1 ＝(∫ A u 2 dA)/(Q 2 A); g is gravitational acceleration.
And (3) dispersing the equations (1) and (2) by adopting a linearized Preissmann four-point hidden format, and solving a discrete equation set by adopting a catch-up method.
1.2 river channel inserting section automatic optimizing model
1.2.1 objective function
Calculating to obtain a calculated value of a hydrologic element (water level and flow) of the observation section through a one-dimensional unsteady flow mathematical model, adopting a Nash coefficient to reflect the coincidence degree of the measured value and the calculated value of the hydrologic element of the observation section, taking the Nash coefficient and the maximum value of the hydrologic element of the observation section as target functions, and expressing as:
wherein i is the serial number of the observation section; n is the total number of observation sections; NSE (i) is a nash coefficient value of the observation section i, and can be expressed specifically as:
wherein T is the calculation period, y t (i) The measured value of the water level (flow) of the section i;
the average value of the measured sequence of the water level (flow) of the section i; />
The value is calculated for the i section water level (flow).
1.2.2 constraint
(1) Maximum water level (flow) error constraint. The objective function of the automatic optimization model of the river channel interpolation section is to obtain the Nash coefficient of the water level (flow rate) and the maximum river channel section interpolation number, position, shape and river channel roughness in the calculation period, which is the comprehensive consideration of the river channel section interpolation number, position, shape and river channel roughness value, and does not exclude the condition that the water level and flow rate error of a certain section in the individual period are overlarge, thus giving the constraint of the maximum water level and flow rate error, namely
Wherein: abs is an absolute function, ε i Is the maximum water level (flow) error of the ith section.
(2) And (5) section spacing constraint. The distance between the inserted sections must not exceed a given maximum distance between the sections, and must not be less than a given minimum distance between the sections, i
L min ≤L(k)≤L max (6)
Wherein L (k) is the section distance between the inserted section k and the previous section, and k=2, 3,4 and 5 in the model; l (L) max For a given maximum section spacing; l (L) min For a given minimum section spacing, it is typically taken as 0.
2 main parameters of model
The number, the position, the shape and the river course roughness of the inserted section can influence the along-path water level and the flow variation of the river to different degrees, so that the main parameters of the automatic optimizing model of the inserted section of the river are the river course roughness, the number, the position and the shape of the inserted section. The shape parameters of the section mainly comprise the bottom width, the river bottom elevation, the slope coefficient and the like because the interpolation section is generally a generalized section (such as a rectangle, a trapezoid, a triangle and the like). The value range of the main parameters can be roughly determined according to the data of the length, the width, the drop and the like of the river channel.
3 model solving method
The model built by the embodiment not only involves more main parameters, but also requires solving a one-dimensional unsteady flow mathematical model each time of optimization, and the san-View south equation set of the one-dimensional unsteady flow mathematical model is a nonlinear equation set, and the solution is needed through continuous iteration. The interaction between the shape and the position of the interpolation section is considered, so that the automatic optimization model of the river channel interpolation section forms a very complex high-dimensional, multivariable and nonlinear optimization problem, and the calculation difficulty is high.
Therefore, in order to reduce the calculation amount and the calculation difficulty, the embodiment uses the interpolation number, position and shape (including the bottom width, the bottom elevation, the slope coefficient and the like) of the river section and the river roughness as state variables, uses the actual measured water level process and the flow process of the observed section as decision variables, and provides a parallel solving method based on a successive approximation method, wherein the main parameters are firstly discretized during calculation, and the number of the interpolation sections is k 1 The number of the position variables is k 2 The shape variable comprises the number of variables such as the bottom width of the section, the elevation of the river bottom, the slope coefficient and the like which are respectively k 3 、k 4 、k 5 The variable number of the river course roughness is k 6 Then share
(i.e. k 1 ×k 2 ×k 3 ×k 4 ×k 5 ×k 6 ) A combination of individual variables; then fixing the number, position and river course roughness values of the inserted sections, and combining the shape variables of the inserted sections (the number of the combined variables is +.>
) Substituting the model for successive optimization, so that the complex multi-section optimization problem is decomposed into a plurality of simple single-section optimization problems, and the solving difficulty of optimizing and calculating the inserting section of the river channel is greatly reduced. However, even if the number of variable combinations is reduced to +>
The calculation amount is still quite large, so the invention combines the OpenMP compiling processing technology designed for single-host multi-core/multi-CPU parallel calculation to parallelize the model and combine variable number +.>
And the calculation is performed simultaneously by being distributed to different threads, so that the calculation efficiency is further improved, and the calculation time is saved.
3.1 "shaped positioning" mode
FIG. 2 is a computational flow diagram of a "shape location" mode; the "shape positioning" mode is to optimize the shape of the inserted section and then determine the position of the inserted section. Firstly, assume that the interpolation sections are equidistantly distributed; then, optimizing and calculating the shape of each interpolation section according to an objective function to obtain shape parameters (bottom width, river bottom elevation and side slope coefficient) of the interpolation section; and finally, in a certain range, optimizing the section spacing of each inserted section to obtain the optimal spacing of each inserted section.
The solution of the 'shape positioning' mode is mainly divided into two stages, wherein the first stage mainly calculates the optimal shape of each interpolation section, and the second stage mainly calculates the optimal position of each interpolation section, and the specific calculation steps are as follows:
3.1.1 shape optimization stage
Step A1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i ，i＝1,2,…,6；
Step A2: determining the river course roughness value;
step A3: determining the number k of the inserted sections 1 The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step A4: setting the optimizing iteration times L=1 of the section shape, and inserting the section j=1;
step A5: to be inserted into section j
Substituting the individual shape parameter combination schemes into the model, carrying out parallel optimizing calculation by combining the river section automatic interpolation optimizing model, and then turning to the step A6;
step A6: fixing the optimized shape parameters of the interpolation section, and then turning to the step A7;
step A7: judging whether the optimizing number of the interpolation section j is equal to the number k of the interpolation sections 1 If not, let j=j+1, go to step A5 again; if yes, obtaining the shape optimization result of each interpolation section and the current shape iteration objective function value F L Turning to step A8;
step A8: judging whether the cross section shape optimizing iteration times L is greater than 1, if not, making L=L+1, and then turning to the step A5; if yes, go to step A9;
step A9: judgment F L And last shape iteration objective function value F L-1 If the two iteration results meet the convergence condition, if not, making L=L+1, and then turning to the step A5; if yes, obtaining an optimal scheme of the shapes of the various inserting sections under the current river course roughness and the number of the inserting sections;
3.1.2 position optimization stage
Step A10: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step A11: fixing the shape of each interpolation section, and for k of interpolation section j 2 Substituting the position parameter scheme into a model, and carrying out parallel optimizing calculation by combining with an automatic interpolation optimizing model of the river section; turning to step A12;
step A12: fixing the optimized position parameters of the interpolation section; turning to step A13;
step A13: judging whether the interpolation section j is equal to k 2 If not, let j=j+1, go to step a11 again; if yes, obtaining the position optimization result of each interpolation section and the current position iteration objective function value F M Turning to step A14;
step A14: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step A11; if yes, go to step A15;
step A15: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A11; if yes, obtaining the optimal scheme of the shape and the position of each interpolation section under the current river course roughness and the number of the interpolation sections, and then turning to the step A16;
step A16: sequentially changing the number of the interpolation sections and the river course roughness value, and repeating the steps A1 to A15 to obtain the optimal scheme of the shape and the position of each interpolation section under the scheme of changing the number of the interpolation sections and the river course roughness value.
3.2 "in bit-shaped" mode
The "shaping in position" mode is to determine the position of the inserted section first and then optimize the shape of the inserted section. Firstly, setting the interpolation sections with enough numbers and identical shapes; then, optimizing calculation is carried out by changing the river bottom elevation of each interpolation section, and the representative interpolation section position is determined according to the calculation result; and finally, optimizing the shape of each interpolation section according to the objective function to obtain the optimal shape parameter of each interpolation section.
The solution in the "bit-shaping" mode is mainly divided into two stages, wherein the first stage mainly calculates representative positions of the interpolation sections, interpolates enough sections in the river channel, and sets the section shape to be rectangular on the assumption that the shape of each section is the same. Then, only changing the river bottom elevation of each section to perform optimizing calculation, and merging sections with similar river bottom elevations so as to select representative positions; in the second stage, the optimal shape of each interpolation section is mainly calculated, and the specific calculation steps are as follows:
3.2.1 position optimization stage
Step B1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i I=1, 2, …, 6;
step B2: determining the river course roughness value;
step B3: determining the number k of rectangular interpolation sections Moment (V) The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step B4: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step B5: substituting the river bottom elevation calculation scheme of the interpolation section j into the model, carrying out parallel optimization calculation by combining with the river section automatic interpolation optimization model, and then turning to the step B6;
step B6: fixing the optimized river bottom elevation of the inserted section, and then turning to the step B7;
step B7: judging whether the optimizing number of the interpolation section j is equal to the number k of the rectangular interpolation sections Moment (V) If not, let j=j+1, go to step B5 again; if yes, obtaining river bottom elevation optimization results of each interpolation section and the current position iteration objective function value F M Turning to step B8;
step B8: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step B5; if yes, go to step B9;
step B9: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A5; if so, obtaining the river bottom elevation change condition of each interpolation section under the current river course roughness and the number of the interpolation sections, merging sections with similar river bottom elevations, and selecting a representative position;
3.2.2 shape optimization stage
The calculation steps are the same as the steps 1-9 of the mode of 'shape positioning'.
A computational flow diagram in "bit-shaping" mode is shown in fig. 3.
The built model and the method are applied to a river channel with the total length of 25.5km, 13 sections are arranged between the model and the D0-D12, wherein the upstream section D0-D1 (including the section D0) lacks the large section data of the river channel, the section needs to be inserted and optimized, and the positions of the inserted sections (D01-D05) are shown in fig. 4.
The section D0 is a river channel inlet section, the section D12 is a river channel outlet section, the mileage between the section D0 and the section D12 is shown in a table 1, and the flow process of the section D0 and the water level process of the section D12 are shown in fig. 5 and 6.
TABLE 1 mileage
The automatic optimization calculation scheme of the 4 river channel interpolation section is as follows:
(1) Number of sections
The number of sections is divided into 2-5, and the number of sections is 4.
(2) River course roughness
Assuming that the roughness of all sections of the river channel is the same, the range of values is 0.034-0.043, and 10 schemes are provided.
(3) Cross-sectional shape
Assuming that the shape of the interpolation section is isosceles trapezoid, passing through the river bottom elevation Z p Three variables of the bottom width B and the slope coefficient m can calculate the water cross section area A, the water surface width B and the change rate of the water surface width along with the water level corresponding to the interpolation cross section
And then combining with a one-dimensional unsteady flow mathematical model to calculate and obtain the river course along-path water level and flow process. The specific relation is shown in formulas (7) to (10), and the schematic diagram of the section shape variable is shown in fig. 7:
A＝(b+m(Z-Z p ))(Z-Z p ) (7)
B＝b+m(Z-Z p ) (8)
m＝cotθ (10)
river bottom elevation Z with given interpolation section shape p And determining the calculation scheme of the section shape optimization by the value ranges of the bottom width b and the slope coefficient m. The value range of the slope angle theta is 2-85 degrees, and the slope angle theta is discretized into 20 values, so that the corresponding discrete values of 20 slope coefficients m can be obtained; the bottom width value range b is 50 m-500 m, and the bottom width value range b is discretized into 10 values; river bottom elevation Z p The value range is 329 m-348 m, and the values are discretized into 20 values, so that 4000 interpolation section shape optimization calculation schemes are calculated in total. The specific parameter values are shown in table 2.
TABLE 2 bottom width b of interpolation section, river bottom elevation Z p And the discrete value of the slope coefficient m
5 "shape location" mode calculation result
The results of the optimization calculation under the conditions of interpolation of 2 to 5 sections with different roughness rates are shown in Table 3 by adopting a pattern positioning mode.
TABLE 3 optimization of calculation results in "shape location" mode
As can be seen from Table 3, in the "in-shape positioning" mode, the objective function values increased with increasing roughness for the interpolation sections of 2 to 5, and were greatest for the roughness of 0.043, 2.778, 2.821, 2.860 and 2.861, respectively. And when the roughness is 0.043, the Nash coefficients of the D0 section water level, the D2 section flow and the D4 section water level are all larger than 0.8 when the number of the inserted sections is 2-5, which shows that a result with higher precision can be obtained in a shape positioning mode. The objective function value is optimal when the number of the inserted sections is 5, and the Nash coefficients of the D0 section water level, the D2 section flow and the D4 section water level are respectively 0.993, 0.958 and 0.910, and the specific calculation results are shown in Table 4.
TABLE 4 optimal calculation results in "shape location" mode
The calculated values and actual measured values of the D0 cross-section water level, the D2 cross-section flow rate, and the D4 cross-section water level in the optimal calculation results of the interpolation 5 cross-sections are shown in FIGS. 8 to 10, respectively. As can be seen from the graph, the simulation effect of the calculated value and the measured value is good, wherein the average relative errors of the D0 section water level, the D2 section flow and the D4 section water level are respectively 0.03%, 6.74% and 0.05%.
6 "calculation result in bit-shaped" mode
And (3) interpolating 117 rectangular sections (including the D0 section) at equal intervals between the D0 section and the D1 section, and performing optimization calculation on the river bottom heights of the 117 interpolation sections to obtain the river bottom elevation parameter change condition of each interpolation section as shown in figure 11.
As can be seen from fig. 11, in the regions from the D0 section mileage of 0m to 700m, 2250m to 3050m, 3450m to 3950m, 4050m to 5200m, and 5350m to 5850m, there is a significant tendency of up-down adjustment of the river bottom elevation of the interpolation section, indicating that the influence of this region on the objective function value is large. Therefore, in this embodiment, 6 representative section positions are selected according to the river bottom elevation adjustment trend of the interpolation section, which are positions 0m, 700m, 3050m, 3950m, 5200m and 5850m from the D0 section, respectively, wherein the first 5 positions are positions corresponding to 5 interpolation sections, and the 6 th position is the position of the D1 section.
Orderly combining representative positions of 5 inserting sections, namely when the number of inserting sections is 2, the number of the inserting section position combinations is 4; when the number of the inserting sections is 3, the number of the position combinations of the inserting sections is 6; when the number of the inserted sections is 4, the number of the combined positions of the inserted sections is 4.
And according to the optimal roughness result of the pattern positioning mode, the roughness value is 0.043, and the section position combinations under different interpolation section numbers are sequentially optimized to obtain the optimal section position combinations under different interpolation section numbers, and the result is shown in table 5.
TABLE 5 optimal section positions for different number of inserted sections
As can be seen from Table 5, except for the inlet section D0 5 (D0) The number of the interpolation sections is increased from 2 to 5 without changing the section positions, and the section interpolation sequence is D0 in sequence 1 、D0 2 、D0 4 And D0 3 。
The results of the optimization calculations at different roughness values are shown in Table 6, given the positions of the sections where 2 to 5 sections are interpolated.
TABLE 6 optimization of calculation results in bit-shaped mode
As can be seen from Table 6, in the "in-position setting" mode, the objective function values increased with increasing roughness for the interpolation sections of 2 to 5, and were greatest for the roughness of 0.043, 2.827, 2.849, 2.860 and 2.863, respectively. And when the roughness is 0.043, the Nash coefficients of the D0 section water level, the D2 section flow and the D4 section water level are all larger than 0.8 when the number of the inserted sections is 2-5, which shows that a result with higher precision can be obtained in a 'setting mode'. The objective function value is optimal when the number of the inserted sections is 5, and the Nash coefficients of the D0 section water level, the D2 section flow and the D4 section water level are respectively 0.996, 0.959 and 0.908, and the specific calculation results are shown in Table 7.
TABLE 7 optimization of calculation results in bit-shaped mode
In the "bitwise setting" optimal calculation results, the calculated values and actual measured values of the D0 cross-sectional water level, the D2 cross-sectional flow rate, and the D4 cross-sectional water level are shown in fig. 12 to 14, respectively. As can be seen from the graph, the simulation effect of the calculated value and the measured value is good, wherein the average relative errors of the D0 section water level, the D2 section flow and the D4 section water level are respectively 0.02%, 6.68% and 0.04%.
7 time consuming calculation
The model is realized on a Microsoft Visual Studio 2019 development platform by adopting a Fortran programming language, and the program is parallelized by using an OpenMP compiling processing technology. The computing program operating environment is: (1) forty-kernel processor Intel (R) Xeon (R) Gold 5218R, main frequency 2.1GHz; (2) 128GB of memory; (3) operating system Windows10 specialty; (4) the configuration manager is x64, release mode. The variable combination number at each optimization in the "shape positioning" mode is 4000, the parallel calculation thread number is 75 in parallel calculation, and the parallel and serial calculation time in the "shape positioning" mode is shown in table 8.
TABLE 8 parallel and serial calculation time consuming (thread count 75) for different number of interpolation sections in "form-located" mode
As can be seen from Table 8, in the "in-shape positioning" mode, when the number of the river channel inserting sections is increased from 2 to 5, the calculated amount is increased, the serial calculation time is increased from 3771.56s to 42870.83s, and the calculation time is increased by 11.37 times. When parallel computing is adopted, the computing time consumption is obviously reduced compared with serial computing, for example, when the number of interpolation sections is 5, the serial computing time consumption is 42870.83s (about 12 h), the parallel computing time consumption is 587.14s (about 10 min), the parallel computing time consumption is only 1.37% of the serial time consumption, the speed is 73.02, and the efficiency is 0.974. Meanwhile, as the number of the interpolation sections is increased, the speed-up ratio and the efficiency of parallel calculation are gradually increased, and the calculation performance is obviously enhanced.
According to the method, a parallel solving method based on a successive approximation method is adopted to solve the river channel interpolation section automatic optimizing model, and the calculation result shows that: (1) The calculated value and the measured value of the 'shape positioning' mode and the 'shape setting' mode are good in simulation effect, nash coefficients of the D0 section water level, the D2 section flow and the D4 section water level in the 'shape positioning' mode are respectively 0.993, 0.958 and 0.910, nash coefficients in the 'shape setting' mode are respectively 0.996, 0.959 and 0.908, and the simulation precision is high; (2) The optimal objective function values in the 'shape positioning' mode and the 'shape setting' mode are 2.861 and 2.863 respectively, the 'shape setting' mode has higher simulation precision than the 'shape positioning' mode, and the 'shape setting' calculation mode of optimizing the section position and then the section shape can better reflect the change characteristics of the river channel; (3) The river channel interpolation section automatic optimization model established by the embodiment has good parallel computing conditions, the computing program is subjected to parallelization processing through the OpenMP compiling processing technology, the computing efficiency can be greatly improved, the computing time is saved, the parallel computing time is not more than 2% of serial time consumption in a shape positioning mode, the maximum speed ratio is 73.02, and the efficiency is 0.974.
The present invention is not limited to the preferred embodiments, and any changes or substitutions that would be apparent to one skilled in the art within the scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (3)
1. The river section automatic interpolation method based on the successive approximation method is characterized by comprising the following steps of:
step 1: establishing a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model by taking the maximum sum of Nash coefficients of observed section water level and flow hydrologic factors as an objective function and taking water level, flow error and section spacing as constraint conditions;
step 2: according to the length, width and ratio drop of the river channel, determining the parameter value range of the automatic interpolation optimization model of the river channel section; the parameters comprise river course roughness, the number of the inserted sections, the positions of the inserted sections and the shape parameters of the inserted sections, wherein the shape parameters of the inserted sections comprise section bottom width, river bottom elevation and slope coefficients;
step 3: according to a parallel solving method based on a successive approximation method, adopting a formal positioning calculation mode or a bit shaping calculation mode to solve an automatic interpolation optimization model of the river section;
the shape positioning calculation mode in the step 3 is to optimize the shape of the interpolation section first and then determine the position of the interpolation section: firstly, assuming equidistant distribution of the interpolation sections, then, carrying out optimization calculation on the shape of each interpolation section according to an objective function to obtain a section bottom width, a river bottom elevation and a slope coefficient, and finally, carrying out optimization calculation on the section spacing of each interpolation section to obtain the optimal spacing of each interpolation section; the method specifically comprises the following steps:
step A1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i ，i＝1,2,…,6；
Step A2: determining the river course roughness value;
step A3: determining the number k of the inserted sections 1 The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step A4: setting the optimizing iteration times L=1 of the section shape, and inserting the section j=1;
step A5: to be inserted into section j
Substituting the individual shape parameter combination schemes into the model, carrying out parallel optimizing calculation by combining the river section automatic interpolation optimizing model, and then turning to the step A6;
step A6: fixing the optimized shape parameters of the interpolation section, and then turning to the step A7;
step A7: judging whether the optimizing number of the interpolation section j is equal to the number k of the interpolation sections 1 If not, let j=j+1, go to step A5 again; if yes, obtaining the shape optimization result of each interpolation section and the current shape iteration objective function value F L Turning to step A8;
step A8: judging whether the cross section shape optimizing iteration times L is greater than 1, if not, making L=L+1, and then turning to the step A5; if yes, go to step A9;
step A9: judgment F L And last shape iteration objective function value F L-1 If the two iteration results meet the convergence condition, if not, making L=L+1, and then turning to the step A5; if yes, obtaining an optimal scheme of the shapes of the various inserting sections under the current river course roughness and the number of the inserting sections;
step A10: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step A11: fixing the shape of each interpolation section, and for k of interpolation section j 2 Substituting the position parameter scheme into a model, and carrying out parallel optimizing calculation by combining with an automatic interpolation optimizing model of the river section; turning to step A12;
step A12: fixing the optimized position parameters of the interpolation section; turning to step A13;
step A13: judging whether the interpolation section j is equal to k 2 If not, let j=j+1, go to step a11 again; if yes, obtaining the position optimization result of each interpolation section and the current position iteration objective function value F M Turning to step A14;
step A14: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step A11; if yes, go to step A15;
step A15: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A11; if yes, obtaining the optimal scheme of the shape and the position of each interpolation section under the current river course roughness and the number of the interpolation sections, and then turning to the step A16;
step A16: sequentially changing the number of the interpolation sections and the river course roughness value, and repeating the steps A1 to A15 to obtain optimal schemes of the shapes and the positions of the interpolation sections under different schemes of the number of the interpolation sections and the river course roughness value;
the bit setting calculation mode in the step 3 is to firstly determine the position of the interpolation section and then optimize the shape of the interpolation section: firstly, setting a plurality of interpolation sections with the same shape, setting the shapes of the sections as rectangles, then, only changing the river bottom elevation of each interpolation section to perform optimizing calculation, merging the sections with similar river bottom elevation, selecting representative positions, and finally, optimizing the shapes of each interpolation section to obtain the optimal shape parameters of each interpolation section; the method specifically comprises the following steps:
step B1: initializing parameters, and determining the value range of each parameter and the number k of each parameter i I=1, 2, …, 6;
step B2: determining the river course roughness value;
step B3: determining the number k of rectangular interpolation sections Moment (V) The method comprises the steps of arranging the interpolation sections at equal intervals, and numbering the interpolation sections according to the sequence from downstream to upstream;
step B4: setting the optimizing iteration times M=1 of the section position, and inserting the section j=1;
step B5: substituting the river bottom elevation calculation scheme of the interpolation section j into the model, carrying out parallel optimization calculation by combining with the river section automatic interpolation optimization model, and then turning to the step B6;
step B6: fixing the optimized river bottom elevation of the inserted section, and then turning to the step B7;
step B7: judging whether the optimizing number of the interpolation section j is equal to the number k of the rectangular interpolation sections Moment (V) If not, let j=j+1, go to step B5 again; if yes, obtaining river bottom elevation optimization results of each interpolation section and the current position iteration objective function value F M Turning to step B8;
step B8: judging whether the section position optimizing iteration number M is greater than 1, if not, enabling M=M+1, and then turning to the step B5; if yes, go to step B9;
step B9: judgment F M And last position iteration objective function value F M-1 If the two iteration results meet the convergence condition, if not, making M=M+1, and then turning to the step A5; if so, obtaining the river bottom elevation change condition of each interpolation section under the current river course roughness and the number of the interpolation sections, merging sections with similar river bottom elevations, and selecting a representative position;
step B10: setting the optimizing iteration times L=1 of the section shape, and inserting the section j=1;
step B11: determining the number k of the inserted sections 1 Substituting the shape parameter scheme of the interpolation section j into the model, carrying out parallel optimization calculation by combining with the river section automatic interpolation optimization model, and then turning to the step B12;
step B12: fixing the optimized interpolation section shape parameters, and then turning to the step B13;
step B13: judging whether the interpolation section j is equal tok 1 If not, let j=j+1, go to step B11; if yes, obtaining the position optimization result of each interpolation section and the current shape iteration objective function value F L Turning to step B14;
step B14: judging whether the cross section shape optimizing iteration times L is greater than 1, if not, making L=L+1, and then turning to the step B11; if yes, go to step B15;
step B15: judgment F L And last shape iteration objective function value F L-1 If the two iteration results meet the convergence condition, if not, making L=L+1, and then turning to the step B11; if yes, obtaining the optimal scheme of the shape and the position of each interpolation section under the current river course roughness and the number of the interpolation sections;
step B16: sequentially changing the number of the interpolation sections and the river course roughness value, and repeating the steps B1-B15 to obtain the optimal scheme of the shape and the position of each interpolation section under the scheme of changing the number of the interpolation sections and the river course roughness value.
2. The automatic river section interpolation method based on successive approximation method according to claim 1, wherein the automatic river section interpolation optimization model in step 1 is:
objective function:
wherein i is the serial number of the observation section; n is the total number of observation sections; NSE (i) is a nash coefficient value of the observation section i, specifically:
wherein T is the calculation period, y t (i) The measured value of the water level or the flow of the section i;
is i section waterAverage value of bit or flow measured sequence; />
Calculating a value for the water level or flow of the section i;
constraint conditions:
wherein: abs is an absolute function, ε i Maximum water level or flow error for the ith section;
L min ≤L(k)≤L max (4)
wherein L (k) is the section distance between the inserted section k and the previous section; l (L) max For a given maximum section spacing; l (L) min For a given minimum section spacing, 0 is taken.
3. The automatic river section interpolation method based on the successive approximation method according to claim 1, wherein the parallel solving method based on the successive approximation method in the step 3 specifically comprises the following steps:
step S1: dispersing the parameters, and setting the number of the interpolation sections as k 1 The number of the inserted section positions is k 2 The number of the bottom widths of the sections in the shape of the inserted section is k 3 The number of river bottom elevations is k 4 The number of the side slope coefficients is k 5 The number of the river course roughness is k 6 Then share
A combination of parameters;
step S2: fixing the number of the inserted sections, the positions of the inserted sections and the value of the river course roughness, and only taking the shape of each inserted section
River section self-substitution based on one-dimensional unsteady flow mathematical model by combining parametersPerforming successive optimization by using a dynamic interpolation optimization model;
step S3: carrying out parallelization processing on a river section automatic interpolation optimization model based on a one-dimensional unsteady flow mathematical model by combining with an OpenMP compiling processing technology designed for single-host multi-CPU parallel computation, and carrying out combination number in the step S2
Assigned to different threads for simultaneous computation.
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